Martin Sorrell
resigned as chief executive of WPP PLC nine months ago following a company probe into his conduct, but his feud with the advertising giant continues.

The company has scrutinized expenses incurred by Mr. Sorrell and charged to the company stretching back several years, including items for an apartment in New York’s Gramercy Park neighborhood, travel for his spouse and child, and ski trips, people familiar with the situation said.

Meanwhile, Mr. Sorrell has launched a rival—albeit smaller—ad firm and has publicly criticized WPP’s strategy, noting its loss of major advertising accounts and questioning decisions made by its new leadership team.

Just this week, in an interview with CNBC at the World Economic Forum in Davos, Mr. Sorrell said that as a large shareholder he was “very concerned” about WPP’s progress and wanted the company to do well.

“Obviously it’s not been an easy period over the last six months or so in relation to major clients and WPP,” he added. WPP’s stock has fallen about 21% since Mr. Sorrell’s departure in April.

Mr. Sorrell, a 73-year-old titan of Madison Avenue who built WPP from a little-known manufacturer of wire shopping carts into a global advertising conglomerate, left in April after a company investigation into an allegation of personal misconduct. The probe addressed whether he used company money for a prostitute, The Wall Street Journal reported in June.

Neither side disclosed the investigation’s findings. Mr. Sorrell said he rejected the allegation of misconduct “unreservedly.” He later denied using company money to pay for a prostitute.

London-based WPP allowed Mr. Sorrell to retire without relinquishing his claim on a long-term bonus, but it hasn’t been paid out.

Under terms of his contract, WPP would need to find “willful gross misconduct” that results in “material economic harm to the company” to justify withholding any payment, a person close to the company said.

Tensions have only risen since his exit, and the question of whether Mr. Sorrell used company funds for personal matters is once again in focus.

WPP contacted Mr. Sorrell late last year, seeking repayment for what it determined to be personal expenses, including travel for his spouse,
Cristiana Falcone Sorrell,
who is a board member at
Viacom Inc.
and
Revlon Inc.

The amounts—about £170,000 ($219,000) in total—aren’t material for WPP, but the company wanted the accounts settled, a person familiar with the situation said. Mr. Sorrell paid the sum requested to WPP, the person added.

In recent weeks, WPP has asked Mr. Sorrell to clarify additional expenses charged to the company that it had scrutinized with the help of an outside firm, including vacations, the person said. If those expenses were found to be improper, they might have to be repaid. The amount in question is larger than the initial bill Mr. Sorrell has paid, the person added.

“We can confirm that an amount has already been received and we have an ongoing dialogue regarding further sums,” a WPP spokesman said Friday.

A spokesman for Mr. Sorrell said: “All Sir Martin’s expenses were regularly scrutinized and approved by WPP management, the audit committee, and the board and were audited annually.”

Ms. Falcone Sorrell didn’t respond to a request to comment.

WPP is now contending with Mr. Sorrell as a competitor in the ad business. His new firm, S4 Capital, last summer outbid WPP for a digital ad-production house. That caused WPP’s lawyers to write to Mr. Sorrell’s lawyers to say he was “in breach of his confidentiality undertakings.”

A WPP spokesman said in July that Mr. Sorrell’s actions had jeopardized his deferred bonus, which is worth millions of pounds. Mr. Sorrell denied the allegation, a spokesman for him said at the time.

The dispute between WPP and Mr. Sorrell is weighing on the company at a delicate time. WPP’s stock is significantly underperforming the broader market, and the advertising giant is wrestling with an industrywide shift to digital ads from print and TV.

Clients have tightened their spending on services from WPP’s agencies, such as J. Walter Thompson and Young & Rubicam, while demanding new services such as data analytics, advertising executives say.

Mark Read,
WPP’s current chief executive, is under pressure to turn the company around. He announced late last year that WPP would shed 3,500 jobs, 2.5% of its workforce.

When Mr. Read was named to the post after a monthslong search, Mr. Sorrell publicly praised Chief Operating Officer
Andrew Scott
as a “very strong, capable executive,” saying he should have been named co-chief executive.

Since leaving the company, Mr. Sorrell has sent messages to Mr. Read, peppering him with suggestions and criticisms, according to people familiar with the matter. Mr. Sorrell also has sent private messages to at least one investor critiquing Mr. Read, according to people familiar with the messages.

In public, Mr. Sorrell, who owns almost 2% of WPP, has picked apart the company’s strategy and bemoaned its recent loss of major advertising business with companies such as
Ford Motor Co.
and
American Express Co.

“Sadly, what seems to be happening at WPP is it seems to be a car crash in slow motion,” Mr. Sorrell told a public-relations conference on Oct. 24.

After WPP decided to sell its stake in Globant, a developer of digital marketing software, Mr. Sorrell told The Sunday Times in September the move was “bordering on negligent.”

WPP has said it appointed Mr. Read sole CEO after evaluating external and internal candidates and sold the Globant stake in line with plans to focus on majority-owned businesses. The company has said the strategy Mr. Read is putting in place is increasingly resonating with clients.

Mr. Sorrell should “not spend half his time publicly and privately either commenting on or, worse, still briefing against everything they are trying to do to turn the company around,” said
Johnny Hornby,
founder of The & Partnership, an agency partly owned by WPP.

A person familiar with Mr. Sorrell’s thinking said he plans for S4 Capital to cherry-pick assets that large ad holding firms like WPP shed as the industry struggles to shore up business.

He also has been focused on acquiring digital firms that are disrupting legacy companies. Last month, S4 Capital acquired MightyHive, a firm that helps advertisers build automated ad buying capabilities internally, allowing them to bypass their ad firms. In-house ad-buying by marketers is a pain point for WPP and its rivals.

During an industry event in November, Mr. Sorrell said he sought no revenge on WPP but added: “The best form of revenge would be building a significant and successful new-era, new-format, new-approach agency,” referring to S4 Capital.